The Franck-Hertz experiment supports Bohr's model

In 1914, James Franck and Gustav Hertz published
the results of an experiment which provided strong
evidence that Bohr's model of atoms with quantized energy
levels was correct.
But, in the haphazard manner of real research,
the authors weren't trying to test Bohr's model;
in fact, they
weren't even aware of Bohr's theory!.
As Franck admitted later

"It might interest you to know that when we made the experiments
that we did not know Bohr's theory.
We had neither read nor heard about it.
We had not read it because we were negligent to read the
literature well enough -- and you know how that happens.
On the other hand, one would think that other people
would have told us about it. For instance,
we had a colloquium at that time in Berlin
at which all the important papers were discussed.
Nobody discussed Bohr's theory.
Why not?
The reasons is that fifty years ago, one was so convinced
that nobody would, with the state of knowledge
we had at that time,
understand spectral line emission,
so that if somebody published a paper about it,
one assumed, "Probably it is not right."
So we did not know it.
But we made that experiment (and got the result
that confirmed Bohr's theory)
because we hoped that if we found out where the
borderline between elastic and inelastic impact
lies ... only one line might appear.
But we did not know whether that would be so,
and we did not know whether at all an emission
of an atom is of such a type that one line
alone can be emitted and all the energy can
be used for that purpose.
The experiment gave it to us,
and we were surprised about it.
But we were not surprised after we read
Bohr's paper later,
after our publication."

-- Excerpt from one of three recordings of J. Franck,
made in connection with a film on the Franck-Hertz
experiment at Educational Services, Inc., Watertown,
Massachusetts, in January, 1961.
As transcribed in "On the recent past of physics",
by Gerald Holton, American Journal of Physics,
vol. 29, p. 805 (1961).

In addition,
Franck and Hertz interpreted their experimental results
incorrectly in the paper below:
they believed that the collisions between electrons and
mercury atoms were ionizing the mercury atoms;
but actually the collisions were exciting
the mercury atoms from their ground n=1 state to the first
excited n=2 state.

Fortunately, other scientists quickly realized how
this experiment did confirm Bohr's hypothesis that
atoms make only certain transitions between discrete
energy states.

So, the idea is that when an electron runs into a mercury
atom, there are two outcomes.
If the incoming electron has a kinetic energy
which is less than the difference
delta E
between
mercury's n=1 and n=2 energy levels,
then it simply bounces off elastically,
keeping all its original kinetic energy:

But if the electron has kinetic energy equal to
(or a bit greater than) delta E,
then it transfers most of its kinetic energy
to the mercury atom, boosting the atom
to the n=2 state.
That leaves the electron with very little kinetic
energy.

Let's look at what happens inside their apparatus.
There's a hot platinum wire at the center (D),
then a wire mesh with a positive voltage (N),
all surrounded by a foil with a small negative voltage (G).
The hot wire spits out electrons ...

However, if we increase the voltage on the wire mesh to a
critical point,
we give the electrons enough kinetic energy that they
can excite mercury atoms from the ground state (n=1)
to the first excited state (n=2) when they collide.

Note the multiple peaks in current, separated
by equal voltages.
These correspond to situations in which
electrons lose most of the kinetic energy in a single
collision,
or in two collisions,
or in three collisions,
and so forth.
Each collision costs the same amount
of energy, because
almost all the mercury atoms are in
the ground state:
the mercury atoms jump back down
from the excited n=2 state to the n=1 state
in a short time.

What is the energy which electrons lose
in each of these collisions?

express as electron-volts

express as Joules

What is the difference in energy levels between
the n=2 and n=1 states of mercury?

express as electron-volts

express as Joules

After it has been excited into the n=2 state
by a collision, the mercury atom very quickly
emits a photon and drops back to the n=1 state.

Q: What is the wavelength of that photon?
Q: What is the color of that photon?

Remember, the last point, number 4, is not quite
correct. The mercury atoms are NOT being
ionized by their collisions with electrons;
they are simply being bumped upwards
into an excited state.